VectorHard
Question
Let 
and 
be two non-colinear unit vectors. If 
and 
, then 
is
and be two non-colinear unit vectors. If and , then is Options
A.
B.
C.
D.
Solution
Let θ be the angle between 
and 
. Since, and are non-collinear vectors, then θ ≠ 0 and θ ≠ π
We have,
= 
= cosc θ
Now,
⇒
⇒
⇒
⇒
⇒
= 1 + cos2 θ - 2 cos2 θ
⇒ = 1 - cos2 θ
⇒ = sin2 θ
Also,
(given)
⇒
⇒
⇒
∴
Now,
∴
and . Since, and are non-collinear vectors, then θ ≠ 0 and θ ≠ π We have,
= = cosc θ
Now,
⇒
⇒
⇒
⇒
⇒
= 1 + cos2 θ - 2 cos2 θ ⇒
= 1 - cos2 θ ⇒
= sin2 θAlso,
(given) ⇒
⇒
⇒
∴
Now,
∴
Create a free account to view solution
View Solution FreeMore Vector Questions
Let P(3, 2, 6) be a point in space and Q be a point on the line . Then the value of μ for which the vector is paral...|(2î + ) × (î + ĵ + ) is equal to -...A parallelogram is constructed on the vectors = 3 − , = + 3. and || = || the angle between and is , then the lengt...If G is centroid of ᐃABC and = , = then bisector equals-...If is along the angle bisector of then -...